Simplify The Expression: ( 6 M 2 − 45 M + 21 ) + ( M − 7 (6m^2 - 45m + 21) + (m - 7 ( 6 M 2 − 45 M + 21 ) + ( M − 7 ]

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. When we simplify an expression, we combine like terms to make it easier to work with. In this article, we will focus on simplifying the given expression: $(6m^2 - 45m + 21) + (m - 7)$. We will use the rules of algebra to combine like terms and simplify the expression.

Understanding the Expression

The given expression is a combination of two expressions: $(6m^2 - 45m + 21)$ and $(m - 7)$. To simplify this expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the terms with the variable $m$.

Combining Like Terms

To combine like terms, we need to follow the rules of algebra. The rules state that we can add or subtract like terms by combining their coefficients. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficients are the numbers that are multiplied by the variable $m$.

Let's start by combining the like terms in the first expression: $(6m^2 - 45m + 21)$. The like terms in this expression are the terms with the variable $m$. The coefficients of these terms are $-45$ and $0$ (since there is no term with $m$ in the expression $6m^2$).

Next, let's combine the like terms in the second expression: $(m - 7)$. The like term in this expression is the term with the variable $m$. The coefficient of this term is $1$.

Simplifying the Expression

Now that we have identified the like terms, we can combine them to simplify the expression. We will add the coefficients of the like terms and keep the variable the same.

The like terms in the first expression are $-45m$ and $0m$. The coefficients of these terms are $-45$ and $0$. When we add these coefficients, we get $-45$.

The like term in the second expression is $m$. The coefficient of this term is $1$.

Now, let's combine the like terms: $-45m + m = -44m$.

The constant terms in the first expression are $21$ and $0$ (since there is no constant term in the expression $6m^2$). The constant term in the second expression is $-7$.

When we add the constant terms, we get $21 - 7 = 14$.

Final Simplified Expression

Now that we have combined the like terms, we can write the final simplified expression:

$6m^2 - 44m + 14$

This is the simplified expression.

Conclusion

In this article, we simplified the given expression: $(6m^2 - 45m + 21) + (m - 7)$. We used the rules of algebra to combine like terms and simplify the expression. We identified the like terms, combined their coefficients, and kept the variable the same. We also added the constant terms to get the final simplified expression. This article demonstrates the importance of simplifying expressions in algebra and provides a step-by-step guide on how to do it.

Tips and Tricks

• When simplifying expressions, always identify the like terms and combine their coefficients.
• Use the rules of algebra to combine like terms.
• Keep the variable the same when combining like terms.
• Add the constant terms to get the final simplified expression.

Frequently Asked Questions

• Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.
• Q: How do I combine like terms? A: To combine like terms, add or subtract their coefficients and keep the variable the same.
• Q: What is the final simplified expression? A: The final simplified expression is $6m^2 - 44m + 14$.

References

• Algebra textbook
• Math website

Related Articles

• Simplifying Expressions with Variables
• Combining Like Terms

Keywords

• Simplifying expressions
• Algebra
• Like terms
• Combining like terms
• Variables
• Coefficients
• Constant terms
  

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Introduction

In our previous article, we simplified the expression: $(6m^2 - 45m + 21) + (m - 7)$. We used the rules of algebra to combine like terms and simplify the expression. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression $2x + 3x$, the terms $2x$ and $3x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients and keep the variable the same. For example, in the expression $2x + 3x$, the coefficients are 2 and 3. When we add these coefficients, we get $2 + 3 = 5$. So, the combined term is $5x$.

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable. For example, in the expression $2x + 3y$, the terms $2x$ and $3y$ are unlike terms because they have different variables.

Q: Can I simplify an expression with variables in the denominator?

A: Yes, you can simplify an expression with variables in the denominator. However, you need to follow the rules of algebra and simplify the expression carefully. For example, in the expression $\frac{2x}{x} + \frac{3}{x}$, the variables in the denominator are $x$. When we simplify this expression, we get $2 + 3 = 5$. So, the simplified expression is $\frac{5}{x}$.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the rules of algebra and simplify the expression carefully. For example, in the expression $\frac{2x}{3} + \frac{3}{4}$, the fractions are $\frac{2x}{3}$ and $\frac{3}{4}$. When we simplify this expression, we need to find a common denominator, which is 12. Then, we can add the fractions: $\frac{8x}{12} + \frac{9}{12} = \frac{8x + 9}{12}$.

Q: Can I simplify an expression with exponents?

A: Yes, you can simplify an expression with exponents. However, you need to follow the rules of algebra and simplify the expression carefully. For example, in the expression $2^3 + 2^2$, the exponents are 3 and 2. When we simplify this expression, we get $8 + 4 = 12$. So, the simplified expression is $12$.

Q: How do I simplify an expression with absolute values?

A: To simplify an expression with absolute values, you need to follow the rules of algebra and simplify the expression carefully. For example, in the expression $|2x| + 3$, the absolute value is $|2x|$. When we simplify this expression, we need to consider two cases: $2x \geq 0$ and $2x < 0$. If $2x \geq 0$, then $|2x| = 2x$. If $2x < 0$, then $|2x| = -2x$. So, the simplified expression is $2x + 3$ if $2x \geq 0$, and $-2x + 3$ if $2x < 0$.

Conclusion

In this article, we answered some frequently asked questions about simplifying expressions. We covered topics such as like terms, combining like terms, unlike terms, expressions with variables in the denominator, expressions with fractions, expressions with exponents, and expressions with absolute values. We hope that this article has been helpful in clarifying some common misconceptions about simplifying expressions.

Tips and Tricks

• Always identify the like terms and combine their coefficients when simplifying an expression.
• Use the rules of algebra to simplify expressions with variables in the denominator, fractions, exponents, and absolute values.
• Consider two cases when simplifying an expression with absolute values: the case when the expression inside the absolute value is non-negative, and the case when the expression inside the absolute value is negative.

Frequently Asked Questions

• Q: What are like terms? A: Like terms are terms that have the same variable raised to the same power.
• Q: How do I combine like terms? A: To combine like terms, add or subtract their coefficients and keep the variable the same.
• Q: What is the difference between like terms and unlike terms? A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

References

• Algebra textbook
• Math website

Related Articles

• Simplifying Expressions with Variables
• Combining Like Terms

Keywords

• Simplifying expressions
• Algebra
• Like terms
• Combining like terms
• Variables
• Coefficients
• Constant terms
• Exponents
• Absolute values
• Fractions